Introduction to Möbius differential geometry

Lecture notes series 300

Udo Hertrich-Jeromin

424 pages, parution le 22/10/2003

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Résumé

This book introduces the reader to the geometry of surfaces and submanifolds in the conformal n-sphere. Various models for Möbius geometry are presented: the classical projective model, the quaternionic approach, and an approach that uses the Clifford algebra of the space of homogeneous coordinates of the classical model; the use of 2-by-2 matrices in this context is elaborated. For each model in turn applications are discussed.

Topics comprise conformally flat hypersurfaces, isothermic surfaces and their transformation theory, Willmore surfaces, orthogonal systems and the Ribaucour transformation, as well as analogous discrete theories for isothermic surfaces and orthogonal systems. Certain relations with curved flats, a particular type of integrable system, are revealed. Thus this book will serve both as an introduction to newcomers (with background in Riemannian geometry and elementary differential geometry) and as a reference work for researchers.

Introduction
Preliminaries: the Riemannian point of view
The projective model
Application: conformally flat hypersurfaces
Application: isothermic and Willmore surfaces
A quaternionic model
Application: smooth and discrete isothermic surfaces
A Clifford algebra model
A Clifford algebra model; Vahlen matrices
Applications: orthogonal systems, isothermic surfaces
Further reading
References
Index

Caractéristiques techniques

	PAPIER
Éditeur(s)	Cambridge University Press
Auteur(s)	Udo Hertrich-Jeromin
Parution	22/10/2003
Nb. de pages	424
Format	15 x 22,7
Couverture	Broché
Poids	575g
Intérieur	Noir et Blanc
EAN13	9780521535694
ISBN13	978-0-521-53569-4